Kubernetes - application-consistent backup
The idea of application-consistent backups is to capture all data in memory and all transactions in process. This is performed by using some type of client software co-resident with the database application to quiesce the database application, flush its memory cache, complete all its writes in order and then perform the backup.
In its turn, Kubernetes operates with specifications of resources (e.g., Deployments, Services, etc.) and their statuses, and in any given time the resource status must be the same as defined in the specification. For storing any important data in Kubernetes, persistent volumes are used. In other words, you cannot perform a backup in an application-consistent manner on Kubernetes, because the main idea of it is different.
It is possible that a specific application for a specific database exists and allows implementing such type of backup. But it is related to that application but not to Kubernetes itself.